Understand Mathematics
Cambridge AS & A Level Mathematics course and assessment guide
Cambridge AS & A Level Mathematics combines secure subject knowledge with application, analysis and clear communication. This guide groups the official syllabus content into a readable learning journey and explains the usual assessment progression.
Know the papers.
Prepare with purpose.
The AS route can be taken as a qualification or as the first part of the full A Level. The final paper combination depends on the subject and entry route.
AS theory
AS candidates demonstrate knowledge, application and interpretation across the AS content.
Practical skills
Sciences include a timetabled practical paper; mathematics assesses technique and problem solving through written papers.
A Level theory
A Level adds more demanding content and unfamiliar applications, requiring linked reasoning across topics.
Planning, analysis and evaluation
Science candidates plan investigations and evaluate evidence; mathematics candidates choose methods and communicate complete solutions.
Every area,
explained clearly.
Pure Mathematics
Pure units develop algebra, functions, coordinate geometry, trigonometry, calculus, vectors and proof.
Algebra and functionsIndices, quadratics, inequalities, transformations and composite functions build symbolic fluency.＋
Indices, quadratics, inequalities, transformations and composite functions build symbolic fluency. Later work extends to partial fractions and more demanding equations.
Coordinate geometryLines, circles and parametric descriptions connect algebra to plane geometry.＋
Lines, circles and parametric descriptions connect algebra to plane geometry. Tangency and intersections require careful simultaneous reasoning.
TrigonometryRadian measure, identities, equations and graphs model periodic behaviour.＋
Radian measure, identities, equations and graphs model periodic behaviour. Advanced units develop compound-angle and double-angle relationships.
Sequences and seriesBinomial expansions, arithmetic and geometric progressions describe patterned change.＋
Binomial expansions, arithmetic and geometric progressions describe patterned change. Convergence and approximation extend the ideas at A Level.
DifferentiationDerivatives describe gradient, rate and turning behaviour.＋
Derivatives describe gradient, rate and turning behaviour. Product, quotient, chain, implicit and parametric methods support increasingly complex functions.
Integration and differential equationsIntegration measures accumulation, area and volume and solves simple differential equations.＋
Integration measures accumulation, area and volume and solves simple differential equations. Substitution, parts and partial fractions expand available methods.
Vectors and complex numbersVectors model lines and spatial relationships, while complex numbers extend algebra and geometry.＋
Vectors model lines and spatial relationships, while complex numbers extend algebra and geometry. Both reward fluent movement between representations.
Applied options
Centres combine Pure Mathematics with Mechanics, Probability & Statistics, or both according to the qualification route.
MechanicsForces, kinematics, momentum, energy and connected particles translate physical situations into mathematical models.＋
Forces, kinematics, momentum, energy and connected particles translate physical situations into mathematical models. Assumptions such as particle, rigid body or smooth plane must be stated and used.
Probability and statisticsData representation, probability, distributions, sampling and hypothesis tests quantify uncertainty.＋
Data representation, probability, distributions, sampling and hypothesis tests quantify uncertainty. Interpretation in context is essential, not an optional final sentence.
Modelling and communicationApplied units require students to define variables, choose assumptions and test results against reality.＋
Applied units require students to define variables, choose assumptions and test results against reality. Complete reasoning matters more than isolated formulas.
A student-friendly summary of the Cambridge International AS & A Level syllabus. Centres should confirm the syllabus version and component option for their examination series.
Content is presented as an original student-friendly explanation. Always use the official syllabus for the examination year as the final authority.